Question: Reduce to lowest terms: $- \dfrac{9}{8} \div - \dfrac{9}{4} = {?}$
Explanation: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{9}{4}$ is $- \dfrac{4}{9}$ Therefore: $ - \dfrac{9}{8} \div - \dfrac{9}{4} = - \dfrac{9}{8} \times - \dfrac{4}{9} $ $ \phantom{- \dfrac{9}{8} \times - \dfrac{4}{9}} = \dfrac{-9 \times -4}{8 \times 9} $ $ \phantom{- \dfrac{9}{8} \times - \dfrac{4}{9}} = \dfrac{36}{72} $ The numerator and denominator have a common divisor of $36$, so we can simplify: $ \dfrac{36}{72} = \dfrac{36 \div 36}{72 \div 36} = \dfrac{1}{2} $